The so-called lemma of d'Alembert [DAH-lum-ber] is an incomplete proof of this statement that can be
The so-called lemma of d'Alembert [DAH-lum-ber] is an incomplete proof of this statement that can be completed using the Weierstrass extreme value theorem. A more direct proof of it uses Rouché's theorem to show that a function with a known number of the values in question has the same number as the function of interest. One corollary of this statement is that every polynomial with only real roots can be written a linear combination of linear and quadratic terms. For 10 points, name this theorem that states that every polynomial over the complex numbers has at least one root, the basic result in an important branch of mathematics.
The so-called lemma of d'Alembert [DAH-lum-ber] is an incomplete proof of this statement that can be completed using the Weierstrass extreme value theorem.
the {fundamental} theorem of {algebra} [prompt on {FTA}]